DFT-D2

In the DFT-D2 method of Grimme the correction term takes the form:

[math]\displaystyle{ E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}} {}^{\prime} \frac{C_{6ij}}{r_{ij,L}^{6}} f_{d,6}({r}_{ij,\mathbf{L}}) }[/math]

where the first two summations are over all [math]\displaystyle{ N_{at} }[/math] atoms in the unit cell and the third summation is over all translations of the unit cell [math]\displaystyle{ {\mathbf{L}}=(l_1,l_2,l_3) }[/math] where the prime indicates that [math]\displaystyle{ i\not=j }[/math] for [math]\displaystyle{ {\mathbf{L}}=0 }[/math]. [math]\displaystyle{ C_{6ij} }[/math] denotes the dispersion coefficient for the atom pair [math]\displaystyle{ ij }[/math], [math]\displaystyle{ {r}_{ij,\mathbf{L}} }[/math] is the distance between atom [math]\displaystyle{ i }[/math] located in the reference cell [math]\displaystyle{ \mathbf{L}=0 }[/math] and atom [math]\displaystyle{ j }[/math] in the cell [math]\displaystyle{ L }[/math] and the term [math]\displaystyle{ f(r_{ij}) }[/math] is a damping function whose role is to scale the force field such as to minimize the contributions from interactions within typical bonding distances. In practice, the terms in the equation for [math]\displaystyle{ E_{\mathrm{disp}} }[/math] corresponding to interactions over distances longer than a certain suitably chosen cutoff radius (VDW_RADIUS, see below) contribute only negligibly to [math]\displaystyle{ E_{\mathrm{disp}} }[/math] and can be ignored. Parameters [math]\displaystyle{ C_{6ij} }[/math] and [math]\displaystyle{ R_{0ij} }[/math] are computed using the following combination rules:

[math]\displaystyle{ C_{6ij} = \sqrt{C_{6ii} C_{6jj}} }[/math]

and

[math]\displaystyle{ R_{0ij} = R_{0i}+ R_{0j}. }[/math]

The values for [math]\displaystyle{ C_{6ii} }[/math] and [math]\displaystyle{ R_{0i} }[/math] are tabulated for each element and are insensitive to the particular chemical situation (for instance, [math]\displaystyle{ C_6 }[/math] for carbon in methane takes exactly the same value as that for C in benzene within this approximation). In the DFT-D2 method, a Fermi-type damping function is used:

[math]\displaystyle{ f_{d,6}(r_{ij}) = \frac{s_6}{1+e^{-d(r_{ij}/(s_R\,R_{0ij})-1)}} }[/math]

whereby the global scaling parameter [math]\displaystyle{ s_6 }[/math] has been optimized for several different DFT functionals such as PBE ([math]\displaystyle{ s_6=0.75 }[/math]), BLYP ([math]\displaystyle{ s_6=1.2 }[/math]) or B3LYP ([math]\displaystyle{ s_6=1.05 }[/math]). The parameter [math]\displaystyle{ s_R }[/math] is usually fixed at 1.00.

The performance of PBE-D2 method in optimization of various crystalline systems has been tested systematically in reference .

Important: It is recommended to use the more advanced and more accurate method DFT-D3.

Usage

The DFT-D2 method is activated by setting IVDW=1 or 10 (or the obsolete LVDW=.TRUE.). Optionally, the damping function and the vdW parameters can be controlled using the following flags (the given values are the default ones):

• VDW_RADIUS=50.0 : cutoff radius (in [math]\displaystyle{ \AA }[/math]) for pair interactions
• VDW_S6=0.75 : global scaling factor [math]\displaystyle{ s_6 }[/math] (available in VASP.5.3.4 and later)
• VDW_SR=1.00 : scaling factor [math]\displaystyle{ s_R }[/math] (available in VASP.5.3.4 and later)
• VDW_SCALING=0.75 : the same as VDW_S6 (obsolete as of VASP.5.3.4)
• VDW_D=20.0 : damping parameter [math]\displaystyle{ d }[/math]
• VDW_C6=[real array] : [math]\displaystyle{ C_6 }[/math] parameters ([math]\displaystyle{ \mathrm{Jnm}^{6}\mathrm{mol}^{-1} }[/math]) for each species defined in the POSCAR file
• VDW_R0=[real array] : [math]\displaystyle{ R_0 }[/math] parameters ([math]\displaystyle{ \AA }[/math]) for each species defined in the POSCAR file
• LVDW_EWALD=.FALSE. : the lattice summation in [math]\displaystyle{ E_{\mathrm{disp}} }[/math] expression is computed by means of Ewald's summation (.TRUE. ) or via a real space summation over all atomic pairs within cutoff radius VDW_RADIUS (.FALSE.). (available in VASP.5.3.4 and later)

Mind: The defaults for VDW_C6 and VDW_R0 are defined only for elements in the first five rows of the periodic table (i.e. H-Xe). If the system contains other elements the user has to define these parameters in INCAR. The defaults for parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available for the PBE (GGA=PE), BP, revPBE, PBE0, TPSS, and B3LYP functionals. If any other functional is used in a DFT-D2 calculation, the value of VDW_S6 (or VDW_SCALING in versions before VASP.5.3.4) has to be defined in INCAR. As of VASP.5.3.4, the default value for VDW_RADIUS has been increased from 30 to 50 [math]\displaystyle{ \AA }[/math]. Ewald's summation in the calculation of [math]\displaystyle{ E_{\mathrm{disp}} }[/math] calculation (controlled via LVDW_EWALD) is implemented according to reference and is available as of VASP.5.3.4.

Related tags and articles

VDW_RADIUS, VDW_S6, VDW_SR, VDW_SCALING, VDW_D, VDW_C6, VDW_R0, LVDW_EWALD, IVDW, DFT-ulg, DFT-D3, DFT-D4

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